The mother of an alleged hostage killer for Islamic State has lost her legal challenge against a Home Office decision to share evidence with the US without seeking assurances that her son and another suspected jihadist terrorist would not face the death penalty.

El Shafee Elsheikh and Alexanda Kotey are accused of belonging to a group of Isis members, nicknamed the Beatles because of their British accents, responsible for killing a number of western captives.

The pair, who have been stripped of their British citizenship, were captured in January last year, prompting a row over whether they should be returned to the UK for a trial or face justice in another jurisdiction.

Elsheikh’s mother, Maha Elgizouli, challenged a decision by the home secretary, Sajid Javid, to share 600 witness statements gathered by the Metropolitan police with US authorities under a mutual legal assistance (MLA) agreement, without seeking assurances that the men would not be executed if they were extradited and tried there.

However, her challenge was rejected on Friday by two high court judges, who ruled the decision was not unlawful.

The lord chief justice, Lord Burnett, sitting with Mr Justice Garnham, said: “There is no general, common law duty on Her Majesty’s government to take positive steps to protect an individual’s life from the actions of a third party, and that includes requiring particular undertakings before complying with the MLA request.”

“Ms Elgizouli hopes that the opportunity will be given for the supreme court to consider whether it has a greater ability to explore the important factors raised in the case she has brought.

“She recognises that they have broader (and fundamental) consequences beyond the case she felt compelled to initiate.

“She did so in the belief that if her son is accused, not that no prosecution should take place, but that any prosecution should respect the established protections that she has believed and still believes exist.”

During a hearing in October, Elgizouli’s lawyers said Javid’s decision, which was outlined in a letter to the then US attorney general, Jeff Sessions, was “unprecedented and unjustified” and put the suspects at risk of an “inhuman punishment”.

Kotey and Elsheikh, who were raised in the UK, are believed to be being detained by Kurdish forces in Syria. They are said to have been members of the cell that also included Mohammed Emwazi, known as “Jihadi John”, who was killed in a US airstrike in 2015, and Aine Davis, who has been jailed in Turkey.

Emwazi appeared in a number of videos in which hostages, including the British aid workers David Haines and Alan Henning, and the US journalists James Foley and Steven Sotloff, were killed.

The Crown Prosecution Service (CPS) decided there was insufficient evidence to prosecute them in the UK.

After Elgizouli launched legal action, the Home Office announced in July that it had agreed to a short-term pause of the MLA process with the US.

Javid faced intense criticism after the letter he wrote to Sessions was leaked, with MPs accusing him of breaching the UK’s longstanding opposition to the death penalty.

The government’s former independent reviewer of terrorism legislation, Lord Carlile, said the move was “extraordinary” and a “dramatic change of policy”.

Theresa May supported Javid’s original decision, which was also backed by Boris Johnson when he was foreign secretary.

Commenting on the court’s decision, Javid said: “My priority has always been to ensure we deliver justice for the victims’ families and that the individuals suspected of these sickening crimes face prosecution as quickly as possible.

“Our longstanding opposition to the death penalty has not changed. Any evidence shared with the US in this case must be for the express purpose of progressing a federal prosecution.”